{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"omni-math","formal_name":"Omni-MATH","introduction":"Omni-MATH evaluates mathematical reasoning on Olympiad-level problems. Its official dataset contains 4,428 problems accompanied by domain and difficulty information.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"3d7fcade-cf67-5fc0-98ee-00affbea016c","task_key":"test--3d7fcade-cf67-5fc0-98ee-00affbea016c","task_revision_id":"1","upstream_id":"","short_description":"Consider the function $f: \\mathbb{N}_{0} \\rightarrow \\mathbb{N}_{0}$, where…","config":"","split":"test","body":"{\"problem\":\"Consider the function $f: \\\\mathbb{N}_{0} \\\\rightarrow \\\\mathbb{N}_{0}$, where $\\\\mathbb{N}_{0}$ is the set of all non-negative integers, defined by the following conditions: (i) $f(0)=0$, (ii) $f(2n)=2f(n)$ and (iii) $f(2n+1)=n+2f(n)$ for all $n \\\\geq 0$. (a) Determine the three sets $L:=\\\\{n \\\\mid f(n)<f(n+1)\\\\}, E:=\\\\{n \\\\mid f(n)=f(n+1)\\\\}$, and $G:=\\\\{n \\\\mid f(n)>f(n+1)\\\\}$ (b) For each $k \\\\geq 0$, find a formula for $a_{k}:=\\\\max \\\\{f(n): 0 \\\\leq n \\\\leq 2^{k}\\\\}$ in terms of $k$.\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://huggingface.co/datasets/KbsdJames/Omni-MATH","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}